Roark, formulas

R. J. Roark, Formulas for Stress and Strain, 3rd ed., McGraw-Hill, New York, 1954. 

Only geometrically simple systems with linear material behavior tend to be calculable by analytical methods. Roark formula for stress and strain (Young and Budynas 2001) is one classical source of information for these structures. When an analytical method can be applied, the calculation can be done in a much simpler and faster way than when numerical methods are applied. Furthermore, the use of computers is not required, although this is not an issue nowadays. 

From Roark formulas for stress and strain P 106 we have ... 

Young, W. C. 1989 Roarke s Formulas for Stress and Strain, 6th Edition. NY McGraw-Hill. 

Buckling is complex to analyse but if we consider the rib as a flat plate, clamped along one edge then Roark gives the formula for the critical buckling stress as... 

Young, W.C. Roark s Formulas for Stress and Strain 5th Edition, McGraw-Hill (1975). 

Roark, R. J., et al., Formula for Stress Strain, McGraw-Hill, 1976. 

In designing a spring, the maximum stress must not exceed the allowable stress or working stress of the material (Roark and Young, 1975). These formulas are useful in the design of vibration isolation systems. 

Young WC, Budynas RG (2002) Roark s formulas for stress and strain, 7th edn. McGraw-Hill, Boston... 

Roark, R. J., and Young, W. C., Formulas for Stress and Strain, 5th Edition, McGraw Hill Book Co., 1975. Burgreen, D., Design Methods for Power Plant Structures, C. P. Press, 1975. 

Ogden R.W. 1997. Non-linear elastic d ormations. Mineola, NY Dover Publications. Roark R.J., R.G. Budynas, and W.C. Young. 2001. Formulas for stress and strain. New York McGraw-Hill. 

Notes 1 The results from the EUROCOMP tables are compared to those obtained using ANSYS and the tables in Roark s Formulae for Stress and Strain. 

Roark s Formulas. Bilayered discs are considered in Roark s formulas. When the bilayered disc is subjected to biaxial moment, the stresses at the top and the bottom surfaces of the disc are given by [36]... 

It should be noted that instead of the actual ring-on-ring tests, the following loading configuration is considered in Roark s formulas. The disc is simply supported at its edge i.e., R = a in Fig. 1(b), and is subjected to a uniform annular line loading at r = Z). In this case, the biaxial moment is related to the load, P, by [36]... 

The moment-load relation has different signs between Eqs. (5) and (8) because of different conventions in defining the moment. Roark s formulas have been adopted by the researchers in the dental community to predict stresses for bilayered dental ceramics subjected to ring-on-ring tests. 

However, because the specimen radius is required to be greater than the support ring radius in actual ring-on-ring tests, it is impractical to use the condition of i = a in Roark s formulas, and modification of Roark s formulas is required. This modification has been considered by Hsueh and Thompson [42], such that for R > a in ring-on-ring tests, the moment-load relation in Roark s formulas i.e., Eq. (8), should be replaced by... 

The modified Roark s formulas, which are pertinent to ring-on-ring tests, can be obtained by combining the biaxial stress-biaxial moment and the biaxial moment-load relations i.e., Eqs. (6a), (6b), and (11). 

Equations (21a) and (21b) can be compared with Roark s formulas. However, while Hsueh etal. s formulas give the stress distribution through the disc thickness, Roark s formulas give only stresses on the top and the bottom surfaces of the disc. For the special case of monolayered discs i. e., n = 1, Hsueh et a/. s formulas become identical to ASTM formulas. 

Fig. 2. The biaxial stress through the thickness of a zirconia monolayered disc subjected to ring-on-ring loading of f = 1000 N showing the comparison among ASTM formulas, Roark s formulas, modified Roark s formulas, Hsueh et al. s formulas, and FEA results.

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